Russian-born mathematician wins math's version of the Nobel

Geometer Mikhail Gromov has won the 2009 Abel Prize, a sort of math analogue to the Nobel Prizes, the Norwegian Academy of Science and Letters announced yesterday. (The Swedes famously do not administer a Nobel in mathematics, so the Norwegians jumped in with the Abel in 2003.) The Russian-born Gromov, 65, of the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France, receives six million Norwegian kroner (about $925,000) as part of the prize. Gromov also holds an appointment at New York University.

The mathematician has extended the notion of shape and distance to seemingly foreign and abstract settings; his work has been essential to the progression of branches of geometry known as Riemann geometry and symplectic geometry. Gromov has also helped pioneer geometric group theory, a discipline that relates geometry to the algebraic field of group theory, and has seen his work push along the theoretical evolution of string theory.

As it happens, Scientific American's own features editor Davide Castelvecchi wrote a PhD thesis at Stanford University, advised by Gromov's friend and colleague Yakov Eliashberg, on a field known as Morse theory that Eliashberg and Gromov helped shape.

"This has been said before," Castelvecchi says, "but Gromov's general approach is to take some kind of problem and soften it. For example, if you have some equation you want to solve, instead of just trying to find the solutions to the equation, you look at the equation as one particular point in a whole landscape of possible problems and possible equations."

Castelvecchi points to a book of Gromov's called Partial Differential Relations as a good indicator of his importance. "There have been people who have done their theses" on single sentences in that book, he says. "You take a page of the book, and each sentence is something he says in an oracular tone.... And each one of those sentences took a whole PhD thesis to prove. It didn't always happen that each of those statements turned out to be true, but this is to give you an idea of how seminal his ideas were. People take one sentence and get whole theories from it."

The mathematician's work "has had a tremendous impact on geometry and has reached from there into major applications in analysis and algebra," George Andrews, the new president of the American Mathematical Society, told ScienceNOW. "One cannot imagine a more worthy recipient."

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